Surface reaction-diffusion kinetics on lattice at the microscopic scale

Chew, Wei-Xiang; Kaizu, Kazunari; Watabe, Masaki; Muniandy, S. V.; Takahashi, Koichi; Arjunan, Satya N.V.

doi:10.1103/physreve.99.042411

Cited by 15 publications

(17 citation statements)

References 91 publications

(93 reference statements)

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“…Our implicit lipid model can be combined with complex networks of protein-protein interactions to efficiently simulate a range of systems involving reversible localization to the membrane, such as models of clathrin-cage assembly [7,35,61,62] and cell polarization [37], or experiments involving binding and oligomerization on membranes [63]. Integration with continuum models of surfaces, as we have done here, is especially critical for developing quantitative and dynamical models of membrane dynamics as they are driven by proteins [64][65][66][67].…”

Section: ⅴ Discussion/conclusionmentioning

confidence: 99%

“…For single-particle binding to surfaces, our method provides critical advantages over existing adsorption methods. Several algorithms for surface adsorption based on discretizing the diffusion equation require short timesteps to provide accurate solutions [12,20,21,37]. Methods using analytical solutions to the diffusion equation with a reactive boundary provide accurate solutions even for larger steps [16,18,19,23,38], but have restricted parameter regimes [16], are model specific [38], and in all cases, are derived only for planar surfaces [12, 16, 18-21, 23, 38] [37].…”

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confidence: 99%

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An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

Yogurtcu

Kothari

et al. 2019

Preprint

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Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites. However, modeling lipid particle populations is expensive. Here we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. Our algorithm can be readily integrated into most reaction-diffusion software packages. We characterize changes to kinetics that emerge from explicit versus implicit lipids as well as surface adsorption models, showing excellent agreement between our method and the full explicit lipid model. Compared to models of surface adsorption, which couple together binding affinity and lipid concentration, our implicit lipid model decouples them to provide more flexibility for controlling surface binding properties and lipid inhomogeneity, and thus reproducing binding kinetics and equilibria. Crucially, we demonstrate our method's application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface, again showing excellent agreement with explicit lipid simulations. Unlike adsorption models, our method retains the ability to bind lipids after proteins are localized to the surface (through e.g. a protein-protein interaction), which can greatly increase stability of multi-protein complexes on the surface. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics. Ⅰ. Introduction:Proteins localize to membranes via multiple different binding modes, including recognition and binding to highly specific lipid head-groups (e.g. PI(4,5)P 2 ) [1], electrostatically driven adherence to negatively charged membranes [2] (as performed by many BAR-domain proteins) [3,4], and binding to membrane-inserted proteins (e.g. Ras) [5,6]. Once proteins have localized to the surface, they can be further stabilized by interactions with additional lipids or transmembrane proteins, and these subsequent binding events are effectively two dimensional (2D) in their search [6,7]. Capturing these various forms of membrane binding is critical for effective kinetic and spatial modeling of cell-scale systems with quantitative comparison to experiment, both in equilibrium and non-equilibrium systems. Because molecular modeling approaches that could capture the fundamental electrostatic or hydrophobic nature of these interactions are too expensive at this scale [8,9], rate-based approaches such as reaction-diffusion provide a powerful alternative [10][11][12][13][14]. These modeling approaches can be us...

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Section: ⅴ Discussion/conclusionmentioning

confidence: 99%

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confidence: 99%

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

Yogurtcu

Kothari

et al. 2019

Preprint

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“…W ij captures the intrinsic reaction rate k ij of the pair according to the Smoluchowski-Collins-Kimball (SCK) model [54,55]. The accuracy and consistency of the bimolecular reaction on lattice in both activation-limited and diffusion-limited regimes have been verified [43,45]. To represent volume occupying molecules, a voxel can be occupied by a single molecule at any given time.…”

Section: Methodsmentioning

confidence: 99%

“…In Spatiocyte, fine and fast-diffusing molecules such as messengers, metabolites and ions are simulated at the compartment scale using the Next-Reaction method [42,44]. The accuracy and consistency of Spatiocyte have been validated in detail recently in both volume [43] and surface [45] compartments. Spatiocyte achieves better execution time scaling behavior compared to other methods [43] because it resolves molecular collisions by looking only at the target voxel for occupancy.…”

Section: Introductionmentioning

confidence: 99%

pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems

Arjunan

Miyauchi

Iwamoto

et al. 2019

Preprint

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Background: Studies using quantitative experimental methods have shown that intracellular spatial distribution of molecules plays a central role in many cellular systems. Spatially resolved computer simulations can integrate quantitative data from these experiments to construct physically accurate models of the systems. Although computationally expensive, microscopic resolution reaction-diffusion simulators, such as Spatiocyte can directly capture intracellular effects comprising diffusion-limited reactions and volume exclusion from crowded molecules by explicitly representing individual diffusing molecules in space. To alleviate the steep computational cost typically associated with the simulation of large or crowded intracellular compartments, we present a parallelized Spatiocyte method called pSpatiocyte. Results: The new high-performance method employs unique parallelization schemes on hexagonal close-packed (HCP) lattice to efficiently exploit the resources of common workstations and large distributed memory parallel computers. We introduce a coordinate system for fast accesses to HCP lattice voxels, a parallelized event scheduler, a parallelized Gillespie's direct-method for unimolecular reactions, and a parallelized event for diffusion and bimolecular reaction processes. We verified the correctness of pSpatiocyte reaction and diffusion processes by comparison to theory. To evaluate the performance of pSpatiocyte, we performed a series of parallelized diffusion runs on the RIKEN K computer. In the case of fine lattice discretization with low voxel occupancy, pSpatiocyte exhibited 74% parallel efficiency and achieved a speedup of 7686 times with 663552 cores compared to the runtime with 64 cores. In the weak scaling performance, pSpatiocyte obtained efficiencies of at least 60% with up to 663552 cores. When executing the Michaelis-Menten benchmark model on an eight-core workstation, pSpatiocyte required 45-and 55-fold shorter runtimes than Smoldyn and the parallel version of ReaDDy, respectively. As a high-performance application example, we study the dual phosphorylation-dephosphorylation cycle of the MAPK system, a typical reaction network motif in cell signaling pathways. Conclusions: pSpatiocyte demonstrates good accuracies, fast runtimes and a significant performance advantage over well-known microscopic particle simulators for large-scale simulations of intracellular reaction-diffusion systems. The source code of pSpatiocyte is available at https://spatiocyte.org.

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Section: Introductionmentioning

confidence: 99%

pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems

et al. 2020

Self Cite

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Background: Studies using quantitative experimental methods have shown that intracellular spatial distribution of molecules plays a central role in many cellular systems. Spatially resolved computer simulations can integrate quantitative data from these experiments to construct physically accurate models of the systems. Although computationally expensive, microscopic resolution reaction-diffusion simulators, such as Spatiocyte can directly capture intracellular effects comprising diffusion-limited reactions and volume exclusion from crowded molecules by explicitly representing individual diffusing molecules in space. To alleviate the steep computational cost typically associated with the simulation of large or crowded intracellular compartments, we present a parallelized Spatiocyte method called pSpatiocyte. Results: The new high-performance method employs unique parallelization schemes on hexagonal close-packed (HCP) lattice to efficiently exploit the resources of common workstations and large distributed memory parallel computers. We introduce a coordinate system for fast accesses to HCP lattice voxels, a parallelized event scheduler, a parallelized Gillespie's direct-method for unimolecular reactions, and a parallelized event for diffusion and bimolecular reaction processes. We verified the correctness of pSpatiocyte reaction and diffusion processes by comparison to theory. To evaluate the performance of pSpatiocyte, we performed a series of parallelized diffusion runs on the RIKEN K computer. In the case of fine lattice discretization with low voxel occupancy, pSpatiocyte exhibited 74% parallel efficiency and achieved a speedup of 7686 times with 663552 cores compared to the runtime with 64 cores. In the weak scaling performance, pSpatiocyte obtained efficiencies of at least 60% with up to 663552 cores. When executing the Michaelis-Menten benchmark model on an eight-core workstation, pSpatiocyte required 45-and 55-fold shorter runtimes than Smoldyn and the parallel version of ReaDDy, respectively. As a high-performance application example, we study the dual phosphorylation-dephosphorylation cycle of the MAPK system, a typical reaction network motif in cell signaling pathways. Conclusions: pSpatiocyte demonstrates good accuracies, fast runtimes and a significant performance advantage over well-known microscopic particle methods in large-scale simulations of intracellular reaction-diffusion systems. The source code of pSpatiocyte is available at https://spatiocyte.org.

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Surface reaction-diffusion kinetics on lattice at the microscopic scale

Cited by 15 publications

References 91 publications

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems

pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems

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